Heavy-traffic asymptotics of a priority polling system with threshold service policy

• The heavy-traffic behavior of a polling system with threshold policy is discussed.
• The scaled queue-length of the critically loaded queue is exponentially distributed.
• Approximations of queue lengths of the stable queues are provided.
• The decay rates of the stable queues are the same decay rate as the classical preemptive priority queues.

In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system with three queues under threshold policy. It turns out that the scaled queue-length of the critically loaded queue is exponentially distributed, independent of that of the stable queues, which possess the same distributions as a two-class priority queue with N-policy vacation. Further, we provide an approximation of the tail queue-length distribution of the stable queues, which shows that it has the same prefactors and decay rates as the classical two-class preemptive priority queue. Stochastic simulations are taken to support the results.